Hi Thomas, Sorry for the delay, busy days, see the mail only now.
> On 22 Oct 2018, at 19:15, Tomas Pales <litewav...@gmail.com> wrote: > > > > On Monday, October 22, 2018 at 1:41:23 PM UTC+2, Bruno Marchal wrote: > > The computable universe hypothesis cannot make sense. To define “computable” > you need to assume arithmetic. But arithmetic executes all computations, and > the measure problem will have to involve infinities. > So the correct passage from “mathematical universe” to computationalism > consists in > > 1) distinguish well the ontology and the phenomenology. Restrict the ontology > to the finite and computable finite objects, > > In his paper, Tegmark included in CUH only mathematical structures defined by > halting computations. So I guess this would include only finite computable > objects? > > > 2) allowing the infinite in the phenomenology, where indeed the physical > universe will appear. > > The infinities ruins physics only if they are put in the ontology. This is > explained in details in basically all my papers (on this subject). I can give > the reference (again) if you are interested. Tegmark missed the mind-body > problem. > > > How do you include the infinite in the phenomenology when you only have > finite objects in ontology? I imagine that we cannot really experience or > perceive the infinite, but we may infer it inductively from finite objects. > And this inductive inference may perhaps give us a kind of feeling or sense > of "the infinite", but it would be a feeling from the inferential process > rather than from the infinite itself. If we are machine at some substitution level, we are duplicable at that level, and this leads to a first person duplication, which itself leads to a reduction of physics to a probability/credibility calculus on all computations going trough our actual relative state. There are infinitely many computations doing that, in arithmetic, so that the first person indeterminacy domain is infinite. Machine are “locally finite” as seen through their histories. > > Anyway, I should tell you that I am no mathematician, so I am afraid I can't > digest the technicalities in your papers. I am not even a physicist or a > professional philosopher, I just dabble in philosophy. My meta-goal consists in showing that with suitable hypothesis, we can proceed with the scientific attitude, in theology/metaphysics/philosophy. Unfortunately, this is not yet well seen in may places. There is no problem with musing and even with metaphysical poetry. Some poet can even be more rdigoruous than philosopher, like with Borges, Valery and Galouye. What cannot be done is to use a personal conviction against a logical argument. That cannot be done with all hypothesis, but with the ChurcTuring thesis, the notion of computation becomes a precise mathematical notion, and we can, by thought experiment and mathematical proof proceed and get results, some of which can lead to testable consequences. > > In my ontological musings, I try to get to the bottom of what is necessary > and avoid arbitrary assumptions. That is the best attitude. > First, what is existence? All definitions of existence should follow the > principle of logical consistency, or in other words, the principle of > identity: an object (that which exists) should be identical to itself. x = x I agree. > It should be what it is and not be what it is not. This also means that the > object should be defined consistently in relation to everything else, > otherwise its identity would be violated. I know there are people who believe > in the existence of inconsistently defined objects (dialetheists), but that > seems like craziness to me, sorry. I rather follow you on this. Paraconsistent logic are interesting for the natural language, and the psychology of lies, but it would be insane to use it in metaphysics, unless a very good argument is provided. > Moreover, unless you arbitrarily block logical explosion, such an > inconsistency would render all ontology meaningless, erasing even the > difference between existence and non-existence. OK. > > So, logical consistency is a necessary criterion of existence. Hmm… I agree that theory of the fundamental things that we will assume has better to be consistent, but that is a meta-assumption. Logical consistency is an attribute of some being, it assumes already some ontology. With the mechanist assumption, we will assume only the numbers, or the combinators, or any basic Turing complete/universal system. Then some machine will be consistent, but some machine can be inconsistent also. Arithmetic if full of inconsistent machines, which eventually get trivial. > Is any other criterion necessary? I don't think so. Adding any other > criterion seems like an arbitrary restriction on what exists. If an object is > identical to itself, then it is something rather than nothing and so it is > there in some sense. Instead of excluding some consistent object from > existence, we can talk about the way in which it exists. With mechanism, the beauty is that we can take a very simple, conceptually, theory. I have recently given the intuitive version, but the formal version is as much simple, you might know it, as it is the theory of combinators (Schoenfinkel, 1924). The language is given by the rule that K is a combinator (expression), and that S is a combinator (expression), and that if x and y are combinator (expression) then (x y) too. By convention, we put only the right parenthesis and not the left one, so ((K K)K) is written KKK, and (K(K K)) is written K(KK). The formal theory is: Identity rules: If x = y and x = z, then y = z If x = y then xz = yz If x = y then zx = zy And the reduction axioms: Kxy = x Sxyz = xz(yz) No other assumptions are made for the basic notion of existence. I could use a simpler language though, like using only the natural numbers 0, S(0), S(S(0)), …. With axioms the laws of addition and multiplication. With mechanism, the theology, including the physics does not depend on the choice of the initial theory. With mechanism, physics has to be derived, and the advantage is that logic can be used to distinguish the truth about the machines, or the numbers, that they can believe, or know, or observe, etc, or not. > And so, we can identify logical consistency with existence, as the property > of all existing objects (there are actually no non-existing objects because > such objects would have to be inconsistent and therefore they would not be > objects but nothing). What happens, is that once you have the numbers (with addition and multiplication), or the combinators, with the reduction laws described above, you get all computations. That determine a flux of consciousness which differentiate in many histories. The observable is what stabilise and get sharable among collection of universal machine, but there is no physical object per se; they are phenomenological. You can read the thread on the combinators, as I will proceed. > > Next, I find that if there are objects, then there must also be relations > between them, as a special kind of objects that hold between other objects. > Relations are just as necessary as the objects between which they hold. And > while relations also hold between other relations, there must also be objects > that are non-relations, as I explained in this thread earlier today. That seems reasonable. > > Next, I find that the most general relation is "similarity", because it is a > relation that holds between any two objects. It means that the two objects > have some different properties and some same properties. Which gives rise to > another general relation called "instantiation", which is the relation > between a property and its instance. The instantiation relation is a special > kind of the similarity relation but less general than similarity since it > doesn't hold between arbitrary two objects. Finally, any objects can define a > collection of them (for example based on their common property, as long as > such a definition is consistent), which gives rise to another general > relation called "composition", which is the relation between a collection and > its part. The composition relation, too, is a special kind of the similarity > relation but less general than similarity since it doesn't hold between > arbitrary two objects. > What you describe looks like the theory of hereditarily finite sets. That is a Turing universal system too. So, those assumption do entail the many dreams of all numbers/machines/combinators, including very long histories. > So, the similarity relation, together with its special kinds - instantiation > and composition, defines all possible relational structures. And all these > three relations come together in set theory, the foundation of mathematics > (instantiation is the satisfaction of a property/predicate by a set and > composition is set membership or the derived relation of set inclusion). More > accurately, by "set theory" I mean all consistent versions of pure set theory. With mechanism, it is better to avoid the axiom of infinity, in the basic ontology. But infinity is very important in all phenomenologies, and in the math needed to handle the finite things. Mechanism is a finitism (no infinite), but is not ultrafinitist, we keep all finite things into account, and that plays a key role in the internal phenomenologies, because it links us to infinitely many “finite things”. > What all versions of pure set theory have in common is the concept of set as > a collection of objects that can be defined by listing those objects (set > members) or by specifying their common property. As it turned out, not every > definition via a common property is consistent, and since it would not be > very useful to define sets only via listing of members, one must also specify > with axioms what common properties can be used to define sets. Which gives > rise to uncountably many axiomatic versions of pure set theory. Yes. I got a sort of canonical topazes through the logic of the first person, but that remains to be studied. Some Russian have studied this a bit, like Artemov. Set theory is a wonderful tool, but category theory too, and many models of the combinator theory are handled through cartesian close category. All this is interesting for the everyday life of the combinators, but the theology, including the extraction of physics, asks for string use of the excluded middle, and the tolerance of the unknown. > > The relational aspect of reality is therefore defined by set theory and in > this sense is mathematical. I don’t really believe in sets. A set is a simplification on the notion of grasping, understanding, it belongs to psychology, indeed universal machine psychology, which is better seen in number, combinator, or partial applicative algebra, when doing theology/metaphysics. > That's where my ontology is the same as Tegmark's mathematical universe idea. With our without the axiom of infinity? > But in my ontology there are also non-relations, which constitute a > non-mathematical aspect of reality. I propose that these non-relations, or at > least some of them, are the qualities of consciousness (qualia), thanks to > their non-relational (unstructured, unanalyzable) nature, which is > nevertheless inseparable from their relations to other objects, some of which > we call "correlates of consciousness”. OK, but computer science and incompleteness shows the existence of true but non believable/provable proposition, although true, and also of non representable relations, or non expressible truth, That is why there is a theology. That is played by the difference of the two Solovay logic G* \ G. What is true about the machine, and what she can justify, + the intensional variants of it. The universal machine has a soul, and the Löbian machine knows that her soul is not a machine ... > > In view of this, why do you restrict your ontology to finite arithmetic and > how do you get qualia from it? I show that if we assume mechanism, physics is constructively reduced to the logic of the points of view developed through the sigma_1 arithmetical reality. Adding an infinity axiom can’t work in the ontology, although it is implied in the phenomenology, like matter, no need to put those things in the ontology, which is kept as simple as possible. It can only be redundant or lead to inconsistency, or lead to inflation of histoires and unpredictability. I can explain, when I will have more time, but meanwhile you can take a look at some of my papers (which all develop some aspect of my phd thesis): Marchal B. The computationalist reformulation of the mind-body problem. Prog Biophys Mol Biol; 2013 Sep;113(1):127-40 Marchal B. The Universal Numbers. From Biology to Physics, Progress in Biophysics and Molecular Biology, 2015, Vol. 119, Issue 3, 368-381. B. Marchal. The Origin of Physical Laws and Sensations. In 4th International System Administration and Network Engineering Conference, SANE 2004, Amsterdam, 2004. http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html (sane04) Plotinus PDF paper link: http://iridia.ulb.ac.be/~marchal/publications/CiE2007/SIENA.pdf Best, Bruno > > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To post to this group, send email to everything-list@googlegroups.com > <mailto:everything-list@googlegroups.com>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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